Exponential Functions And Logarithms Worksheet
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4Algebra IIA
Unit IV: Exponential Functions and Logarithms
• Foundational Material
o Use the properties of exponents to simplify
o Solve problems and fit data using linear and
expressions
quadratic and polynomial models
o Perform inverse operations
• Goal
o Study exponential functions
o Study logarithms, the inverse
o Solve problems and fit data
and use properties of
of exponents and logarithmic
to exponential and
exponents
functions
logarithmic models
• Why?
o To further build a foundation for higher level mathematics such as statistics and business calculus
o These skills can be used to observe, understand, and model relationships in science, social studies and economics
o Maximize and minimize area and volume
• Key Vocabulary
o Asymptote
o Exponential Growth
o Logarithmic Function
o Base
o Exponential Equation
o Logarithmic Regression
o Change of Base Formula
o Exponential Regression
o Natural Logarithm
o Common Logarithm
o Inverse Function
o Properties of Logarithms
o Exponential Decay
o Logarithmic Equation
Lesson 2: Logarithmic Functions and Properties of Logarithms
• Write equivalent forms for exponential and logarithmic functions. (CC.9-12.F.BF.5)
• Write, evaluate and graph logarithmic functions. (CC.9-12.F.IF.7e)
• Use properties to simplify logarithmic expressions.
• Translate between logarithms in any base.
How many times would you have to double $1 to have $8? _____
!
The equation that models this situation is ! = 1 2
.
How many times would you have to double $1 to have $512? Rather than actually figuring this out, there is
an operation that will allow us to do this quickly, finding a logarithm.
A logarithm is the exponent to which a specified base must be raised to obtain a given value. The algebraic
relationship between exponential equations and logarithmic equations follows.
Both equations have a 'b', the base, an x, and a y.
These two equations are equivalent, just like these
two equations are equivalent: y = x + 9 and y - 9 = x.
Using algebra you can get from one to the other.
“Angle Method”
log
x = y
Write in exponential form:
b
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